sin a + cos b =√2
sin b + cos a =√2
Найти sin(a+b) и cos(a+b)

sina+cosb=√2sinb+cosa=√2sin(a+b)=?;cos(a+b)=?1)sin(a+b)=sinacosb+cosasina(sina+cosb)²=2+(sinb+cosa)²=2sin²a+2sinacosb+cos²b+sin²b+2sinbcosa+cos²a=42+2(sinacosb+cosasinb)=4sinacosb+cosasinb=1sin(a+b)=1a+b=π/2+2πk;k€z2)cos(a+b)=0